Numerical Analysis Using Nonlinear Least-Square Fit function of the form f(t) = Asin(Bt) + Ccos(Dt) to fit 24 data points

Asked Sep 30 '13 at 17:21

Active Nov 26 '15 at 10:58

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can anybody help me solve this problem. As I am stuck at the $E(A,B,C,D)=\sum_{k=1}^{24} (f(t_k)-y_k)^2 $ also $E_2 (f)=? $ is the root mean square error

I am having difficulty finding the correct bestfitcurve as I arbitraririly chose initial [A,B,C,D] = [1,1,1,1] and the curve I generated was very sinusoidal. I also used t=linspace(0,2*pi,24) since this is a data within a 24-hour cycle. Here is my octave code

    function z=E(u)
x=linspace(0,2*pi,24);
y=[66 66 65 64 63 63 62 61 60 60 59 58 58 58 58 58 57 57 57 58 60 64 67 68];
A=u(1);
C=u(2);
B=u(3);
D=u(4);
z=0;
    for i=1:24
        z = z+(A*sin(B*x(1,i))+C*cos(D*x(1,i)) - y(1,i))^2;
    end
end
P=fmins('E',[1,1,1,1]) P=-1.072785   61.164715    2.844565    0.015377
plot(x, P(1)*sin(P(3)*x) + P(2)*cos(P(4)*x), "-;fun;", x, y, "+;datapts;")

fun=(x,function(x)); datapts=(x,y)

edited Sep 30 '13 at 18:06

asked Sep 30 '13 at 17:21

user182936

I think you should use a model equation like $f(t)=A\sin(Bx+C)+D\cos(Ex+F)$ instead of yours – Ömer Sep 30 '13 at 17:52
But won't the addition of arbitrary parameters make things more complicated? – user182936 Sep 30 '13 at 18:09
May be but your function does not seem well suited for your data. – Ömer Sep 30 '13 at 18:13

Numerical Analysis Using Nonlinear Least-Square Fit function of the form f(t) = Asin(Bt) + Ccos(Dt) to fit 24 data points

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